Logan (his first name was also spelled “Greenberry”) was born into slavery, but he was later freed by his white father, David Logan. After moving to Missouri, Logan married Judah Duncan, and the couple had five children. In Feb. 1831, Logan became one of the first African Americans to settle in Texas. Several months later, he received a grant of land in Chocolate Bayou in Austin's third colony, now Brazoria County, where he leased a blacksmith shop on the Francis Bingham plantation.

Logan enlisted in the Texas army on Oct. 7, 1835, in order to fight for Texan independence. He fought in the Battle of Concepción, and in the siege of Bexar he received a wound that left his right arm crippled for life. In 1836, he bought a house in Brazoria, which he turned into a boarding house for members of the new Texas congress meeting in Columbia.